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If the earth were to suddenly contract t...

If the earth were to suddenly contract to half of its present radius (without any external torque on it), by what duration would the day be decreased ? Assume earth to be perfect solid sphere of radius `(2)/(5)MR^(2)`.

Text Solution

Verified by Experts

The correct Answer is:
18
Present radius of the earth, `R_(1)=R`
New radius of the earth after contraction , `R_(2)=R//2`
`T_(1)=24h`, `T_(2)=?`
By conservation of angular momentum,
`I_(1)omega_(1)=I_(2)omega_(2)` or `(2)/(5)MR_(1)^(2).(2pi)/(T_(1))=(2)/(5)MR_(2)^(2).(2pi)/(T_(2))`
or `T_(2)=((R_(2))/(R_(1)))^(2).T_(1)=((R//2)/(R))^(2)xx24=(1)/(4)xx24=6h`
`:.` Decrease in the duration of the day
`=24-6=18h`.
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